AP Calculus BC Quiz
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INFINITE SEQUENCES AND SERIES
Question 1
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∑
n
=
1
∞
n
2
n
+
1
\sum_{n=1}^{\infty} \frac{n^2}{n+1}
∑
n
=
1
∞
n
+
1
n
2
, what does the nth-term test imply about divergence?
A
The series converges because
lim
n
→
∞
n
2
n
+
1
=
0
\lim_{n\to\infty}\frac{n^2}{n+1}=0
lim
n
→
∞
n
+
1
n
2
=
0
.
B
No conclusion can be drawn because the limit is infinite.
C
The series diverges because
lim
n
→
∞
n
2
n
+
1
≠
0
\lim_{n\to\infty}\frac{n^2}{n+1}\neq 0
lim
n
→
∞
n
+
1
n
2
=
0
.
D
The series converges because polynomials cancel.
E
The series diverges because the terms are rational.
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